Parallelogram mnpq was dilated to create parallelogram m'n'p'q'. which statements are true about the parallelograms? check all that apply. the length of side mn is 2 units. the length of side m'n' is 5 units. the image is smaller than the pre-image. sides mq and m'q' both have the same slope, 1. the scale factor is 2/5

Options 1,2 and 4 are correct.

Step-by-step explanation:

We have been given a parallelogram MNPQ was dilated to create parallelogram  M'N'P'Q' and we asked to find out which of the given options are correct.

Let us see all the options one by one.

On using distance formula we can see that side MN is 2 units.

Therefore,option 1 is correct.

We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.

Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.

Now look at our option 4.

Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.

Therefore, option 4 is correct indeed.

Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.

Therefore, our fifth option is false.

Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

Slope = vertical distance / horizontal distance = change in y / change in x.

Scale factor = length of image/corresponding length of pre-image.

Find the length of MN:

MN = |4 - 2| = 2 units (Option A is true).

Find M'N':

M'N' = |10 - 5| = 5 units (Option B is true).

MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).

Find Slope of MQ:

Slope = 1/1 = 1

Find Slope of M'Q':

Slope = 2/2 = 1 (Option D is true).

Find the scale factor:

Scale factor = dimension of image/dimension of pre-image = M'N'/MN

Scale factor = 5/2 (Option E is NOT true).

Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

Learn more about scale factor on:

link

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.